! File: submodule_standard_tpo_formulation_analysis.f90 ! Authors: Francesco Torsello (FT) !************************************************************************ ! Copyright (C) 2020-2023 Francesco Torsello * ! * ! This file is part of SPHINCS_ID * ! * ! SPHINCS_ID is free software: you can redistribute it and/or modify * ! it under the terms of the GNU General Public License as published by * ! the Free Software Foundation, either version 3 of the License, or * ! (at your option) any later version. * ! * ! SPHINCS_ID is distributed in the hope that it will be useful, * ! but WITHOUT ANY WARRANTY; without even the implied warranty of * ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * ! GNU General Public License for more details. * ! * ! You should have received a copy of the GNU General Public License * ! along with SPHINCS_ID. If not, see . * ! The copy of the GNU General Public License should be in the file * ! 'COPYING'. * !************************************************************************ SUBMODULE (standard_tpo_formulation) analysis !**************************************************** ! !# Implementation of the methods of TYPE ! tpo_formulation that analyze a grid function. ! ! FT 12.07.2021 ! !**************************************************** IMPLICIT NONE CONTAINS MODULE PROCEDURE analyze_constraint !**************************************************** ! !# Count on how many grid points the argument 'constraint' ! has values lying in the intervals \( (-oo,10^{-7}], ! [10^{-7},10^{-6}], ! [10^{-6},10^{-5}], [10^{-5},10^{-4}], [10^{-4},10^{-3}], ! [10^{-3},10^{-2}], [10^{-2},10^{-1}], [10^{-1},1], ! [1,10^1], [10^1,10^2], [10^2,10^3], ! [10^3,+oo) \) ! ! FT ! !**************************************************** USE constants, ONLY: pi USE utility, ONLY: determinant_sym3x3, zero, one, two, four, ten IMPLICIT NONE INTEGER:: cnt_m7, cnt_m6, cnt_m5, cnt_m4, cnt_m3, cnt_m2, cnt_m1, cnt_0, & cnt_p1, cnt_p2, cnt_p3, cnt_oo, grid_points, i, j, k, & unit_analysis, nx, ny, nz DOUBLE PRECISION:: total, dx, dy, dz, detg3 LOGICAL:: exist !LOGICAL, PARAMETER:: DEBUG= .FALSE. IF( this% export_constraints_details )THEN ! !-- Export the constraint analysis to a formatted file ! unit_analysis= 20120 INQUIRE( FILE= TRIM(name_analysis), EXIST= exist ) IF( exist )THEN OPEN( UNIT= unit_analysis, FILE= TRIM(name_analysis), & STATUS= "REPLACE", & FORM= "FORMATTED", & POSITION= "REWIND", ACTION= "WRITE", IOSTAT= ios, & IOMSG= err_msg ) ELSE OPEN( UNIT= unit_analysis, FILE= TRIM(name_analysis), STATUS= "NEW", & FORM= "FORMATTED", & ACTION= "WRITE", IOSTAT= ios, IOMSG= err_msg ) ENDIF IF( ios > 0 )THEN PRINT *, "... error when opening " // TRIM(name_analysis), & ". The error message is", err_msg STOP ENDIF !CALL test_status( ios, err_msg, "...error when opening " & ! // TRIM(name_analysis) ) WRITE( UNIT = unit_analysis, IOSTAT = ios, IOMSG = err_msg, & FMT = * ) & "# Run ID [ccyymmdd-hhmmss.sss]: " // run_id WRITE( UNIT= unit_analysis, IOSTAT = ios, & IOMSG = err_msg, FMT = * ) & "# The rows contain the points (l,x,y,z), with l refinement level, ", & "at which ", name_constraint, & " has values in: (-oo,1D-7], [1D-7,1D-6], [1D-6,1D-5], [1D-5,1D-4]" & // ", [1D-4,1D-3], [1D-3,1D-2], [1D-2,1D-1], [1D-1,1], [1,1D+1]" & // ", [1D+1,1D+2], [1D+2,1D+3], [1D+3,+oo)" ENDIF CALL this% abs_values_in( zero, 1.0D-7, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m7 ) CALL this% abs_values_in( 1.0D-7, 1.0D-6, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m6 ) CALL this% abs_values_in( 1.0D-6, 1.0D-5, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m5 ) CALL this% abs_values_in( 1.0D-5, 1.0D-4, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m4 ) CALL this% abs_values_in( 1.0D-4, 1.0D-3, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m3 ) CALL this% abs_values_in( 1.0D-3, 1.0D-2, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m2 ) CALL this% abs_values_in( 1.0D-2, 1.0D-1, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_m1 ) CALL this% abs_values_in( 1.0D-1, 1.0D0, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_0 ) CALL this% abs_values_in( 1.0D0, 1D+1, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_p1 ) CALL this% abs_values_in( 1.0D+1, 1.0D+2, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_p2 ) CALL this% abs_values_in( 1.0D+2, 1.0D+3, constraint, l, & this% export_constraints_details, & unit_analysis, cnt_p3 ) CALL this% abs_values_in( 1.0D+3, HUGE(DBLE(one)), constraint, l, & this% export_constraints_details, & unit_analysis, cnt_oo ) CLOSE( UNIT= unit_analysis ) IF( this% export_constraints_details )THEN PRINT *, " * The details about the absolute values of ", & name_constraint, " are printed to ", name_analysis ENDIF nx= this% get_ngrid_x(l) ny= this% get_ngrid_y(l) nz= this% get_ngrid_z(l) dx= this% get_dx(l) dy= this% get_dy(l) dz= this% get_dz(l) grid_points= nx*ny*nz ! !-- Compute the l2 norm of the constraints ! l2_norm= zero !$OMP PARALLEL DO DEFAULT( NONE ) & !$OMP SHARED( nx, ny, nz, constraint ) & !$OMP PRIVATE( i, j, k ) & !$OMP REDUCTION( +: l2_norm ) DO k= 1, nz, 1 DO j= 1, ny, 1 DO i= 1, nx, 1 l2_norm= l2_norm + constraint(i,j,k)*constraint(i,j,k) ENDDO ENDDO ENDDO !$OMP END PARALLEL DO l2_norm= SQRT( l2_norm/grid_points ) ! !-- Compute a rough estimate of the integral of the constraints ! integral= zero IF( PRESENT(source) )THEN !$OMP PARALLEL DO DEFAULT( NONE ) & !$OMP SHARED( nx, ny, nz, dx, dy, dz, this, & !$OMP constraint, source, l ) & !$OMP PRIVATE( i, j, k, detg3 ) & !$OMP REDUCTION( +: integral ) DO k= 1, nz, 1 DO j= 1, ny, 1 DO i= 1, nx, 1 CALL determinant_sym3x3( & this% g_phys3_ll% levels(l)% var(i,j,k,:), detg3 ) integral= integral & + dx*dy*dz*SQRT(detg3)*( constraint(i,j,k) - source(i,j,k) ) ENDDO ENDDO ENDDO !$OMP END PARALLEL DO ELSE !$OMP PARALLEL DO DEFAULT( NONE ) & !$OMP SHARED( nx, ny, nz, dx, dy, dz, this, & !$OMP constraint, l ) & !$OMP PRIVATE( i, j, k, detg3 ) & !$OMP REDUCTION( +: integral ) DO k= 1, nz, 1 DO j= 1, ny, 1 DO i= 1, nx, 1 CALL determinant_sym3x3( & this% g_phys3_ll% levels(l)% var(i,j,k,:), detg3 ) integral= integral & + dx*dy*dz*SQRT(detg3)*constraint(i,j,k) ENDDO ENDDO ENDDO !$OMP END PARALLEL DO ENDIF integral= integral/(two*four*pi) ! !-- Compute the loo norm (supremum norm) of the constraints ! loo_norm= zero !$OMP PARALLEL DO DEFAULT( NONE ) & !$OMP SHARED( nx, ny, nz, constraint ) & !$OMP PRIVATE( i, j, k ) & !$OMP REDUCTION( MAX: loo_norm ) DO k= 1, nz, 1 DO j= 1, ny, 1 DO i= 1, nx, 1 loo_norm= MAX( loo_norm, ABS( constraint(i,j,k) ) ) ENDDO ENDDO ENDDO !$OMP END PARALLEL DO ! !-- Write a summary of the results to the logfile ! WRITE( UNIT= unit_logfile, FMT = * ) "# The absolute values of ", & name_constraint, & " on the gravity grid are in the following intervals, on the ", & "given percentage of grid points:" WRITE( UNIT= unit_logfile, FMT = * ) "" WRITE( UNIT= unit_logfile, FMT = "(A15,F5.1,A1)" ) " (-oo,1D-7]: ", & ten*ten*DBLE(cnt_m7)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-7,1D-6]: ", & ten*ten*DBLE(cnt_m6)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-6,1D-5]: ", & ten*ten*DBLE(cnt_m5)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-5,1D-4]: ", & ten*ten*DBLE(cnt_m4)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-4,1D-3]: ", & ten*ten*DBLE(cnt_m3)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-3,1D-2]: ", & ten*ten*DBLE(cnt_m2)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-2,1D-1]: ", & ten*ten*DBLE(cnt_m1)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D-1,1]: ", & ten*ten*DBLE(cnt_0)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1,10]: ", & ten*ten*DBLE(cnt_p1)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (10,1D+2]: ", & ten*ten*DBLE(cnt_p2)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D+2,1D+3]: ", & ten*ten*DBLE(cnt_p3)/DBLE(grid_points) , "%" WRITE( UNIT = unit_logfile, FMT = "(A15,F5.1,A1)" ) " (1D+3,+oo]: ", & ten*ten*DBLE(cnt_oo)/DBLE(grid_points), "%" WRITE( UNIT = unit_logfile, FMT = * ) WRITE( UNIT = unit_logfile, FMT = * ) "# l2-norm of ", name_constraint,& " over the gravity grid= ", l2_norm WRITE( UNIT = unit_logfile, FMT = * ) WRITE( UNIT = unit_logfile, FMT = * ) "# Integral of ", name_constraint,& " over the gravity grid= ", integral WRITE( UNIT = unit_logfile, FMT = * ) WRITE( UNIT = unit_logfile, FMT = * ) & "# loo-norm (supremum of the absolute values) of ", & name_constraint,& " over the gravity grid= ", loo_norm WRITE( UNIT = unit_logfile, FMT = * ) total= ten*ten*DBLE(cnt_m7)/DBLE(grid_points) + & ten*ten*DBLE(cnt_m6)/DBLE(grid_points) + & ten*ten*DBLE(cnt_m5)/DBLE(grid_points) + & ten*ten*DBLE(cnt_m4)/DBLE(grid_points) + & ten*ten*DBLE(cnt_m3)/DBLE(grid_points) + & ten*ten*DBLE(cnt_m2)/DBLE(grid_points) + & ten*ten*DBLE(cnt_m1)/DBLE(grid_points) + & ten*ten*DBLE(cnt_0) /DBLE(grid_points) + & ten*ten*DBLE(cnt_p1)/DBLE(grid_points) + & ten*ten*DBLE(cnt_p2)/DBLE(grid_points) + & ten*ten*DBLE(cnt_p3)/DBLE(grid_points) + & ten*ten*DBLE(cnt_oo)/DBLE(grid_points) IF( total - ten*ten > 1.0D-4 )THEN PRINT *, " * WARNING! The percentages of the absolute values of ", & name_constraint, & " in the given intervals do not sum up to 100%. ", & " They sum up to", total, "%" PRINT *, "Check what happens in the SUBROUTINES analyze_constraint ", & "and abs_values_in." ENDIF END PROCEDURE analyze_constraint MODULE PROCEDURE abs_values_in !************************************************** ! * ! Set "cnt" equal to the number of times that the * ! absolute value of "constraint" is in * ! (lower_bound,upper_bound]. * ! Depending on "export", it prints to file the * ! grid points at which this happens. * ! * ! FT 24.03.2021 * ! * !************************************************** USE tensor, ONLY: jx, jy, jz IMPLICIT NONE INTEGER:: i, j, k, nx, ny, nz nx= this% get_ngrid_x(l) ny= this% get_ngrid_y(l) nz= this% get_ngrid_z(l) cnt= 0 DO k= 1, nz, 1 DO j= 1, ny, 1 DO i= 1, nx, 1 IF( ABS( constraint(i,j,k) ) >= lower_bound .AND. & ABS( constraint(i,j,k) ) < upper_bound )THEN cnt= cnt + 1 IF( export )THEN WRITE( UNIT= unit_analysis, IOSTAT = ios, & IOMSG = err_msg, FMT = "(F17.13)", & ADVANCE= "NO" ) &!"(E15.6)" & l WRITE( UNIT= unit_analysis, IOSTAT = ios, & IOMSG = err_msg, FMT = "(F17.13)", & ADVANCE= "NO" ) &!"(E15.6)" & this% coords% levels(l)% var( i, j, k, jx ) WRITE( UNIT= unit_analysis, FMT= "(A2)", & ADVANCE= "NO" ) " " WRITE( UNIT= unit_analysis, IOSTAT = ios, & IOMSG = err_msg, FMT = "(F17.13)", & ADVANCE= "NO" ) & this% coords% levels(l)% var( i, j, k, jy ) WRITE( UNIT= unit_analysis, FMT= "(A2)", & ADVANCE= "NO" ) " " WRITE( UNIT= unit_analysis, IOSTAT = ios, & IOMSG = err_msg, FMT = "(F17.13)", & ADVANCE= "NO" ) & this% coords% levels(l)% var( i, j, k, jz ) WRITE( UNIT= unit_analysis, FMT= "(A2)", & ADVANCE= "NO" ) " " ENDIF ENDIF ENDDO ENDDO ENDDO IF( export .AND. cnt == 0 )THEN WRITE( UNIT= unit_analysis, FMT= "(I1)", ADVANCE= "NO" ) 0 WRITE( UNIT= unit_analysis, FMT= "(I1)", ADVANCE= "NO" ) 0 WRITE( UNIT= unit_analysis, FMT= "(I1)", ADVANCE= "NO" ) 0 ENDIF !WRITE( UNIT= unit_analysis, FMT= * ) "" END PROCEDURE abs_values_in END SUBMODULE analysis